Measurement of the CKM Angle Alpha at the BABAR Detector Using B Meson Decays to Rho Final States

This thesis contains the results of an analysis of B0 → ρ+ρ- using 232 million Υ(4S) → B(bar B) decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. From a fitted signal yield of 617 ± 52 events, the longitudinal polarizations fraction, fL, of the decay is measured to be 0.978 ± 0.014(stat)-0.029+0.021(syst). The nearly fully longitudinal dominance of the B0 → ρ+ρ- decay allows for a measurement of the time dependent CP parameters SL and CL, where the first parameter is sensitive to mixing induced CP violation and the second one to direct CP violation. From the same signal yield, these values are found to be SL = -0.33 ± 0.24(stat)-0.14+0.08(syst) and CL = - 0.03 ± 0.18(stat) ± 0.09(syst). The CKM angle α is then determined, using these results and the branching fractions and polarizations of the decays B0 → ρ0ρ0 and B+ → ρ+ρ0. This measurement is done with an isospin analysis, in which a triangle is constructed from the isospin amplitudes of these three decay modes. A χ2 expression that includes the measured quantities expressed as the lengths of the sides of the isospin triangles is constructed and minimized to determine a confidence level on α. Selecting the solution compatible with the Standard Model, one obtains α = 100o ± 13o